In this study, I examine the alternating-offer bilateral bargaining model with private correlated values. The correlation of values is modeled via the global games information structure. I focus on the double limits of perfect Bayesian equilibria as offers become frequent and the correlation approaches perfect. I characterize the Pareto frontier of the double limits and show that it is efficient, but the surplus split generally differs from the Nash Bargaining split. I then construct a double limit that approximates the Nash Bargaining split in the ex-post surplus, but with a delay. Further, I prove the Folk theorem when the range of the buyer's values coincides with the range of the seller's costs: any feasible and individually rational ex-ante payoff profile can be approximated by a double limit.